vorlesung funktionalanalysis ii “ (functional analysis ii) · vorlesung ” funktionalanalysis ii...
TRANSCRIPT
Vorlesung”Funktionalanalysis II “
(Functional Analysis II)
I. Unbounded Operators in Hilbert Spaces.General Theory
§1. Closed Operators 1
§2. The Graph of a Linear Operator 7
§3. Hermitian Operators 12
II. Spectral Theory of Selfadjoint Operators
§1. The Resolvent of Selfadjoint Operators 24
§2. Spectral Families 30
§3. Stieltjes’s Inversion Formula. FurtherProperties of Functions of Bounded Variation 45
§4. Integral Representation of the Resolvent 61
§5. Fundamental Properties of the Funktion ρ(.; f, g) 69
§6. The Spectral Theorem for Selfadjoint Operators 79
§7. The Spectrum of a Selfadjoint Operator 87
§8. Functions of a Selfadjoint Operator. The Heinz-Kato Inequality 115
References 133
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